 In this lecture what we will be doing is we'll be taking a look at a number of different problem-solving tips for the gas power cycles that we've looked at in the course and the ones it will be covering will be the auto cycle, the diesel, the Stirling and the Brayton. So the first one that we will start with is the auto cycle. So there's the PV as well as the TS diagram for the auto cycle. Now typically when you're solving one of these problems you'll have some information. Usually you'll know the compression ratio but what I'll do is I'll walk you through some of the different steps and show you how the equations come about that are used for solving these problems. So the first comment is that if you know the compression ratio what you'll want to do is you want to look up in tables that you would have in the back of your book. The tables we'll be talking about would be ideal gas properties of air and it would be one where you would have the relative volume, specific volume, as well as relative pressure. We'll talk about that in a moment when we look at the diesel as well as the Brayton. But you would want the table with the relative specific volume and if we look back at our process what we notice is going from one to two and then from three to four these are isentropic processes and consequently we can take advantage of that when we're solving these problems. So if you start by knowing the inlet temperature so that would be your atmospheric air temperature you would go to the table for the properties of air. You would get the relative specific volume at state one and it turns out that the ratio of relative specific volumes is equal to the ratio of the specific volumes at state one to state two which we said was the compression ratio for the engine and consequently once you know VR1 from the tables in the back of the book you can then go and the compression ratio you can then get VR2 and then go back into the table again and get temperature at two. Now once we have temperature at two so that would be the temperature at this point so we would know this temperature we can then use the ideal gas law to get the pressure. You will not always know the pressure you'll know the compression ratio but you will not know the pressure so let's take a look at how we can use the ideal gas law for that. So we know rho is P over RT we can rearrange that in terms of the gas constant so with this we know that the gas constant will not be changing and so we can say that P2 specific volume at two T2 equals P1 specific volume at one and T1 and consequently that gives us a relationship with which we can then work to get the pressure. So the other thing that we want to do let's take a look at what's going on during both the heat addition and the heat rejection processes so that's going from state 2 to state 3 and then state 4 to state 1 and of note is the fact that this is taking place where we have constant specific volume so the volume is not changing during these processes and so we will take advantage of that by looking at the first law. So let's start with 2 to 3. So we're writing out the first law and this is for a fixed mass control volume. Now the work in this equation here if you recall back to when we talked about the first law for fixed mass we said that the work be work other plus boundary work and the boundary work was defined as being PDV. Well if we have fixed volume that is going to be zero and consequently that term disappears and the work term here disappears. And then what we're left with is Q in is equal to U3 so the internal energy at 3 minus the internal energy at 2 and similarly we can write for Q out so that is the heat rejection process. It is equal to the change in internal energy between state 4 and 1 and finally the network from our cycle can be computed by Q in minus Q out. So those are a number of different equations that you can use. Each problem is going to be a little different because you'll have different information given to you but you may wonder when you look at solutions that you may see within any of your thermodynamics books how they're getting particular combinations especially this component here neglecting the boundary work but that is how they're getting the equations and those are the ones that you can use then to solve problems involving the auto cycle.